Abstract
Bootstrapping the mean, variance, standard error of the mean, regression coefficient and its standard error is considered. It is shown that at a fixed sample size bootstrap estimates converge to classical sample estimates as the number of bootstrap replications tends to infinity. For the mean, variance and regression coefficient, convergence almost everywhere is proven; for the standard error of the mean and standard error of the regression coefficient, weak convergence is proven. The speed of convergence is illustrated by simulation results.
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Čepar, D., Radalj, Z. Some asymptotic behaviour of the bootstrap estimates on a finite sample. Statistical Papers 31, 41–46 (1990). https://doi.org/10.1007/BF02924672
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DOI: https://doi.org/10.1007/BF02924672